8.2.P2

Developing intuition about how electric fields connect to forces, electric potential, and electric potential energy is not always easy. The goal of this task is to focus on developing the connections across these concepts.

1) Let's start by reviewing the connection between force and potential energy. How are these concepts conceptually linked? Mathematically linked?

2) Now describe the relationship between the force and the electric field. Again, how are they related conceptually and mathematically?

3) Finally, let's add the electric potential. Describe the connection between electric potential and potential energy as well as the electric field.

4) The result is what we affectionately refer to as the Big Square. The Big Square helps us to recall the connections between the electric force, electric field, electric potential, and electric potential energy. Now that we've articulated the connections between these concepts, let's try to apply them.

Situation A) We have two infinitely long uniformly charged plates (ignore the effects of gravity). An electron is released from rest at point a at time t=0.

i) How does the electric field compare at points a and b? How does the potential compare?

Using the connections from the Big Square, plot the following:

ii) The x-component of the electric field E_{x} as a function of x

iii) The x-component of the electric force F_{x} on the electron as a function of x

iv) The electric potential V as a function of x

v) The electric potential energy U of the electron as a function of x

vi) How would your responses to (i) - (v) change if the charge was positive?

Situation B) We have two infinitely long uniformly charged plates (ignore the effects of gravity). An electron is traveling to the right at 10 m/s when it reaches point a at time t=0. Some time later it reaches point b.

i) What is the direction of the velocity at point b?

Using the connections from the Big Square, plot the following:

ii) The x-component of the electric field E_{x} as a function of x

iii) The x-component of the electric force F_{x} on the electron as a function of x

iv) The y-component of the electric field E_{y} as a function of y

v) The y-component of the electric force F_{y} on the electron as a function of y

vi) The electric potential V as a function of y

vii) The electric potential energy U of the electron as a function of y

Bonus! You can also go back to these situations and create energy bar charts accounting for the energy (including kinetic) over time.

Vashti Sawtelle 2/22/12

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